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Assertion (A): The slope deflection method is a stiffness method in which the joint displacements are found by applying the equilibrium conditions at each joint. Reason (R): The displacements at a joint of a member are independent of the displacements of the member at the far end of the joint.

Assertion (A): The slope deflection method is a stiffness method in which the joint displacements are found by applying the equilibrium conditions at each joint. Reason (R): The displacements at a joint of a member are independent of the displacements of the member at the far end of the joint. Correct Answer Both A and R are true is not a correct explanation of A

Explanation:

Slope- Deflection Method:

  • It is the stiffness method in which the displacements (rather than forces) are taken as unknown quantities. 
  • The unknown displacements are obtained by solving equations of equilibrium (rather than equations of compatibility) that contain coefficients in the form of stiffnesses.
  • In this method, if the slopes at the ends and the relative displacement of the ends are known, the end moment can be found in terms of slopes, deflection, stiffness, and length of the members. 
  • In this method all joints are considered rigid; i.e the angle between members at the joints is considered a not to change in value as loads are applied.
  • Distortion, due to axial and shear stresses, being very small, are neglected.
  • The degree of freedom of a structure is the number of independent joint displacements. Thus,  the displacements at a joint of a member are independent of the displacements of the member at the far end of the joint  

Hence, Both above statements are true but they are not explaining each other. 

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